A location invariant moment-type estimator. I

Cheng Xiu Ling, Zuoxiang Peng, Saralees Nadarajah

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4 Citations (Scopus)


The moment’s estimator (Dekkers et al., 1989) has been used in extreme value theory to estimate the tail index, but it is not location invariant. The location invariant Hill-type estimator (Fraga Alves, 2001) is only suitable to estimate positive indices. In this paper, a new moment-type estimator is studied, which is location invariant. This new estimator is based on the original moment-type estimator, but is made location invariant by a random shift. Its weak consistency and strong consistency are derived, in a semiparametric setup.

Original languageEnglish
Pages (from-to)23-31
Number of pages9
JournalTheory of Probability and Mathematical Statistics
Publication statusPublished - 2008
Externally publishedYes


  • Extreme value index
  • Location invariant property
  • Moment estimation
  • Order statistics
  • Regular varying functions
  • Strong and weak consistencies

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